Sweet Potato Pie

Preheat the oven to 350 °F. Prick the sweet potatoes with a fork and roast them on a shallow baking pan in the middle of the oven until very tender, about 1 1/4 hours. Cool to room temperature. Raise the oven temperature to 400 °F, and place a shallow baking pan on the bottom rack. Scoop the flesh from potatoes into a bowl and discard the skins. Mash the sweet potatoes with a fork until smooth. Melt the butter in a small saucepan and stir in the sugar. Add the melted butter mixture to the sweet potatoes with the milk and the eggs and beat with a whisk until smooth. Whisk in the remaining ingredients (the filling will be quite liquid). Pour the filling into the pie shell. Carefully transfer the pie to the heated shallow baking pan on the bottom rack of the oven and bake until the filling is just set, about 40 minutes. Transfer the pie to a rack to cool.